
Convergence in distribution implies convergence of the CDF [1]}, which in turn implies convergence of quantiles at every point of continuity of the limiting CDF [2]}. By continuity everywhere of the normal CDF this implies that for any \(\alpha \in (0,1)\) :
\( \frac{c_{h,b}(\alpha )}{\sqrt{ \nabla h(\hat{\theta }_n) V_n \nabla h(\hat{\theta }_n)^\prime /n }} - q(\alpha ) \overset{p}{\rightarrow } 0,\) 
